The puzzle is as follows:
In 2012, which began on a Sunday, Marina was happy because her birthday was on a Saturday and she celebrated it with her friends. We know, Marina was born in a year where there were more Fridays and Saturdays than other days of the week, and that the day of the week she was born was the twentieth time that appeared in that year. If in 2012 she turned between 20 to 29 years old, in what date she was born?
The choices given are:
- May 19th
- May 20th
- May 16th
- May 18th
I found this puzzle in my book Logic challenges. From the way it is presented it seems to have been adapted from either a reprinted version from Martin Gardner's Puzzle Carnival book of the late 1970s or Raymond Smullyan's What's the name of this book.
I don't know what's the intended meaning when it mentions that a pair of days appear more times in a year.
I assume that this situation happens when these days are contiguous such as in this case Friday and Saturday. It appears that when this happens such year begins with January 1st being Friday, and such year is not a leap year.
This hidden piece of information is not very obvious to me and I don't know if there is any way to prove it. Neither I know if I am in the right path.
I'm not sure how to use that the day of the week she was born appeared the twentieth time.
Can someone help me here? I'm looking for a step-by-step explanation of how to get to the answer.
According to my book the official answer is choice 1, or May 19th. But I have no idea how to get there.
How can I solve this without much fuss? More importantly, is my observation about the dates appearing more times in a calendar correct?